Results 31 to 40 of about 15,357 (262)
Graphs and Combinatorics, 2017 The {\em power index} $Θ(Γ)$ of a graph $Γ$ is the least order of a group $G$ such that $Γ$ can embed into the power graph of $G$. Furthermore, this group $G$ is {\em $Γ$-optimal} if $G$ has order $Θ(Γ)$. We say that $Γ$ is {\em power-critical} if its order equals to $Θ(Γ)$. This paper focuses on the power indices of complete graphs, complete bipartite
Xuanlong Ma, Min Feng 0004, Kaishun Wang
openaire +4 more sources
The Electronic Journal of Combinatorics, 2011 For a graph $G$, its $r$th power is constructed by placing an edge between two vertices if they are within distance $r$ of each other. In this note we study the amount of edges added to a graph by taking its $r$th power. In particular we obtain that, for $r\geq 3$, either the $r$th power is complete or "many" new edges are added.
openaire +6 more sources
A Random Graph Model for Power Law Graphs [PDF]
Experimental Mathematics, 2001 We propose a random graph model which is a special case of sparserandom graphs with given degree sequences which satisfy a power law. This model involves only a small number of paramo eters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. From these parameters, various properties of the
Aiello, William, Chung, Fan, Lu, Linyuan
openaire +2 more sources
Quotient graphs for power graphs [PDF]
Rendiconti del Seminario Matematico della Università di Padova, 2017 In a previous paper of the first author a procedure was developed for counting the components of a graph through the knowledge of the components of one of its quotient graphs. Here we apply that procedure to the proper power graph \mathcal{P}_0(G ...
BUBBOLONI, DANIELA +2 more
openaire +3 more sources
Graph Powering and Spectral Robustness
SIAM Journal on Mathematics of Data Science, 2020 Spectral algorithms, such as principal component analysis and spectral clustering, typically require careful data transformations to be effective: upon observing a matrix $A$, one may look at the spectrum of $ψ(A)$ for a properly chosen $ψ$. The issue is that the spectrum of $A$ might be contaminated by non-informational top eigenvalues, e.g., due to ...
Abbe, Emmanuel +3 more
openaire +2 more sources
d-Path Laplacians and Quantum Transport on Graphs
Mathematics, 2020 We generalize the Schrödinger equation on graphs to include long-range interactions (LRI) by means of the Mellin-transformed d-path Laplacian operators.
Ernesto Estrada
doaj +1 more source
Clawfreeness of the powers of a graph
Discrete Applied Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Patrick Bahls, Nicole A. Gin
openaire +2 more sources
Note On The Game Colouring Number Of Powers Of Graphs
Discussiones Mathematicae Graph Theory, 2016 We generalize the methods of Esperet and Zhu [6] providing an upper bound for the game colouring number of squares of graphs to obtain upper bounds for the game colouring number of m-th powers of graphs, m ≥ 3, which rely on the maximum degree and the ...
Andres Stephan Dominique, Theuser Andrea
doaj +1 more source
The Edit Distance Function of Some Graphs
Discussiones Mathematicae Graph Theory, 2020 The edit distance function of a hereditary property is the asymptotically largest edit distance between a graph of density p ∈ [0, 1] and . Denote by Pn and Cn the path graph of order n and the cycle graph of order n, respectively. Let C2n*C_{2n}^* be
Hu Yumei, Shi Yongtang, Wei Yarong
doaj +1 more source
Power Domination in Graphs [PDF]
, 2020 In this chapter, we are interested in power domination in graphs. Power domination is a variation of domination introduced to address a physical problem of monitoring a network with phasor measurement units. The originality of this variation is that some propagation happens, and the set of covered vertices results from an iterative process.
openaire +3 more sources